Ethereal, I know. Not only do they look absolutely gorgeous, they are also an useful feature extraction technique for identifying lines or curves in an image. It works like this: imagine all the pixels in an original image (a) are sorted by a sift (b) such that only pixels that lie on a certain line can pass through. These pixels are then collected in a designated spot on the transformed image(c). Repeat this for all the lines you can possibly draw in this 2D space – every direction and every position. What you get at the end is a Hough Transform (c).
Fact: Hough Transform sorts image pixels into a gorgeous picture.
In case you were wondering, here are the original images for the beauties above.
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Bright spots (intersections of curves) on the transformed image indicate how many prominent lines there are in the original image. For example, there are 7 bright spots in the 2nd transformed image, for the 7 edges forming the T shaped object (two of them lie on the same line).
Math is fun, and pretty.
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